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User blog:Alejandro Magno/Make an extension of the Notation! (my style)
Remake of Aarex's Game. Rules are the same as Aarex's Version: http://googology.wikia.com/wiki/User_blog:Googleaarex/Make_an_extension_of_the_notation New rules: 1. You can't edit previous definitions Post your entries in the comments! Extension 0 (original) (mine) 0#n = n+n 1#n = 0#(0#(0#(...(0#(0#(0#n)))...))) with n levels m#n = m-1#(m-1#(m-1#(...(m-1#(m-1#(m-1#n)))...))) with n levels Extension 1 (mine) (0)#n = n#n (0)0#n = (0)#n (0)1#n = (0)1#((0)1#((0)1#(...((0)1#((0)1#((0)1#n)))...))) with n levels (0)(0)#n = (0)n#n (1)#n = (0)(0)(0)...(0)(0)(0)#n with n (0)'s (1)(1)#n = (1)(0)(0)(0)...(0)(0)(0)#n with n (0)'s (2)#n = (1)1#((1)1#((1)1#(...((1)1#((1)1#((1)1#n)))...))) with n levels (m)#n = (m-1)m-1#((m-1)m-1#((m-1)m-1#(...((m-1)m-1#((m-1)m-1#((m-1)m-1#n)))...))) with n levels Extension 2 (mine) ((0))#n = (n)#n ((0)0)#n = ((0))#n ((0)1)#n = ((0))((0))((0))...((0))((0))((0))#n with n ((0))'s ((0)(0))#n = ((0)n)#n ((1))#n = ((0)(0)(0)...(0)(0)(0))#n with n (0)'s etc. We can have ((2)), ((m)), (((0))), (((1))), ((((0)))), (((((0))))), etc. Limit is (((...(((m)))...)))#n Extension 3 (Sbiis) (0,1)#n = (((...(((n)))...)))#n w/n ()s (1,1)#n = (0,1)(0,1)...(0,1)#n w/n (0,1)s etc. (0,2)#n = (((...(((n,1),1),1)...,1)#n w/n ,1s (0,(0))#n = (0,n)#n (0,0,1)#n = (0,(0,(0,(0, ... (0,n))...))#n w/n 0,s ... (0,0,0,1)#n = (0,0,(0,0,(0,0,(0,0,( ... (0,0,n))...))#n w/n 0,0,s etc. Extension 4 (mine) (011)#n = (0,0,0,...,0,0,1)#n with n entries (111)#n = (011)(011)(011)...(011)(011)(011)#n with n (011)'s ((0)11)#n = (n11)#n (0,111)#n = ((((...(((n)))...)))11)#n with n levels etc. Then: (012)#n = (0,0,0,...,0,0,111)#n with n entries (01(1))#n = (01n)#n (010,1)#n = (01(((...(((n)))...))))#n with n levels etc. Then: (01011)#n = (010,0,0,...,0,0,1)#n with n entries (0101011)#n = (01010,0,0,...,0,0,1)#n with n entries etc. Limit is (010101...0101011)#n Extension 5 (Aarex) Extension 5: (021)#n = (010101...101011)#n with n entries (022)#n = (010101...10101121)#n with n entries (02021)#n = (02010101...101011)#n with n entries (031)#n = (020202...202021)#n with n entries (0m1)#n = (0m-10m-10m-1...m-10m-10m-11)#n with n entries (0(0)1)#n = (0n1)#n etc. Limit is (0[(0[(0...1)]1)]1)#n Extension 6 (Aarex) (00,11)#n = (0[(0[(...[(0[(0n1)]1)]...)]1)]1)#n /w n 0's (01,11)#n = (00,100,100,1...0,100,100,11)#n with n 0,1-spaces (00,21)#n = (0[(0[(...[(0[(0n,11),1]1),1]...),1]1),1]1)#n /w n 0's (00,0,11)#n = (0[0,(0[0,(...[0,(0[0,(00,n1)]1)]...)]1)]1)#n /w n 1's (0[011]1)#n = (00,0,0,...,0,0,11)#n /w n entries inside [] (0[00,11]1)#n = (0[0[(0[0[(...[0[(0[0[(0[0n1]1)]1]1)]...1])]1]1)]1)#n /w n 0's Limit of extension 6 is (0[0[0...1]1]1) Extension 7 (mine/Aarex) Extension 7a (0,11)#n = (0[0[0...1]1]1)''#n with n levels (1,11)#n = (0,11)(0,11)(0,11)...(0,11)(0,11)(0,11)#n with (0,11)'s etc. (00,111,11)#n = (0[0[0...1]1]1,11)#n with n levels (0,12)#n = (0[0[0...1]1]1,12)#n with n levels (0,12)#n = (0[0[0...,111,11]1,11]1,11)#n with n levels (0,10,11)#n = (0,10[0,10[0,100,1...1]1]1)#n with n levels (0112)#n = (0,10,10,1...,10,10,11)#n with n ,1-spaces (0,21)#n = (0[0[0...11]11]11)#n with n levels Extension 7b (0,0,11)#n = (0,(0,(...(0,(0,n1)1)...)1)1)#n with n levels etc. (0,0,111)#n = (0,0[0,0[0,0...11]11]11)#n with n levels etc. Limit is (0,0,0,...111)#n Extension 8 (Aarex) To make extension 8, let change ab into ab. (00011)#n = (00[00[00...1]1]1)#n /w n nested (00021)#n = (00[00[00...11]11]11)#n /w n nested (000011)#n = (000[000[000...1]1]1)#n /w n nested Limit is (000...011)#n. Extension 9 (mine) Extension 9a (00,11)#n = (000...011)#n with n entries (01,11)#n = (00,100,100,10...00,100,100,11)#n with n 0,1's etc. (00,21)#n = (000...01,11)#n with n entries etc. (00,0,11)#n = (00,00...011)#n with n entries etc. Extension 9b (00[ 1 ]11)#n = (00,0,0,...,0,0,11)#n with n entries (00[ 2 ]11)#n = (00[ 1 ]0[ 1 ]0[ 1 ]...[ 1 ]0[ 1 ]0[ 1 ]11)#n with n entries etc. (00[ 0 ][ 1 ]11)#n = (00[ [00[ [00[ [...0[ [00[ [00[ 1]11] ]11] ]1...] ]11] ]11] ]11)#n with n levels etc. Limit is (00[ 0 ][ 0 ][ 0 ]...[ 0 ][ 0 ][ 1 ]11)#n Category:Blog posts